She was an art student at the time, a witness to a police crackdown on a social protest movement in the town of San Salvador Atenco 11 years ago. Then she became a victim.

Ms. Jiménez, now 34, embarked on a decade-long struggle for justice that is finally moving closer to resolution. The Inter-American Court of Human Rights is considering the case of Ms. Jiménez and 10 other women who were sexually abused, tortured and jailed, their lives irrevocably altered.

In an accusation that has become emblematic of human rights violations by the police in Mexico, the women are seeking accountability from the people who ordered the crackdown on the protests and tolerated its abuses — a group they say includes President Enrique Peña Nieto. At the time, Mr. Peña Nieto was the governor of Mexico State, where the crackdown took place.

Her hands clasped, Ms. Jiménez told a court last month that the police beatings had broken her fingers and that the pain had forced her to quit art school. She still struggles to sleep.

Bárbara Italia Méndez testified that officers had dragged her to the back of a bus, before “all hell started.”

The assailants ripped off her underwear, grabbed her breasts and beat her with nightsticks. They penetrated her with fingers and called out to the officers at the front of the bus to join in, she said.

Thrown into jail, Ms. Méndez, now 38, was denied gynecological attention even after she reported the sexual assault. When a doctor arrived to stitch a bleeding head wound, she said, he did not use anesthesia.

As she cried out in pain, the doctor laughed and replied, “Suck it up.”

Five of the 11 women testified at the court hearing in San José, Costa Rica, where the court is based. The Mexican government was due to send its final arguments, which are not public, by Sunday, and the court is expected to issue a ruling next year.

In making their case against Mr. Peña Nieto, the women’s lawyers cited written testimony they said he had given to the Supreme Court during an investigation in 2009. Not only did he order the police crackdown, they said, he also “learned about police abuse” at the time.

“When he was asked about what actions he had taken the moment he learned about the situation, he does not mention having taken any concrete measure to make the unfolding abuses stop,” one of the lawyers said.

The lawyers did not provide details about what information Mr. Peña Nieto learned, and it is impossible to independently confirm the statements because the Supreme Court testimony is not publicly available.

The Mexican government, in a written statement Monday, rejected the claim that he knew of the abuses. In the initial phase of the crackdown on the protesters, the statement said, there was “no concrete evidence of abuses or violations of human rights.” It said Mr. Peña Nieto had ordered an investigation into what happened the moment he learned about it.

The women’s lawyers said, “The Supreme Court concluded that the violence in Atenco was encouraged and permitted by the chain of command.” But in its final resolution, the Mexican court chose not to hold Mr. Peña Nieto and other high-ranking officials responsible for the abuses.

If the women’s battle lays bare how routine police torture has become in Mexico, it also reveals the impunity torturers often enjoy when victims try to hold them and their supervisors to account.

Speaking for the Mexican government at the hearing, Miguel Ruiz Cabañas, the undersecretary for foreign relations, admitted that the abuse had taken place. But he argued that women had no “objective data” to show that the beatings and torture had been carried out under a direct order or that they had been a “state strategy.”

In an admission that the abuse had occurred, the federal government offered to pay reparations to the women in 2013. The women refused the money and scholarships and pressed for a full investigation.

Mr. Ruiz Cabañas rejected the women’s argument that the crimes had gone unpunished, pointing to what he called an “exhaustive investigation” by the Supreme Court. But he admitted that none of the 52 people originally arrested in the women’s case — mostly police and jail officials — had been convicted.

“The victims have asked for every one of those who are allegedly responsible to be investigated,” Mr. Ruiz Cabañas told reporters. “The investigation, although it is not finished, is on its way and is very far advanced.”

The testimony by Mr. Ruiz Cabañas seemed not to convince the judges, who asked how, with no convictions, the government can argue that there is no impunity.

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Claudia Hernández, center-left, and Suhelen Gabriela Cuevas Jaramillo at a hearing last month. They are among 11 Mexican women seeking justice at the Inter-American Court of Human Rights.CreditJuan Carlos Ulate/Reuters

In its final ruling, the Inter-American Court could order the Mexican government to carry out a new investigation, under guidelines to examine the chain of command above the police, said Santiago Aguirre, deputy director of the Agustin Pro Juárez Center for Human Rights in Mexico City, which represents the women. Such a ruling could raise new problems for Mr. Peña Nieto.

The case goes back to a violent police operation to dislodge flower vendors who were protesting in the central square of San Salvador Atenco.

Two people were killed and 200 detained in the two-day clash. Of those, 40 were women who were pushed onto buses and driven to jails hours away.

Unable to obtain justice in Mexico, 11 took their case to the Inter-American Commission of Human Rights in Washington, which agreed that the Mexican authorities had not investigated the abuse properly. The commission demanded a more thorough inquiry and sent the case to the court.

For the women — some activists and students, others housewives or vendors who happened to be in the square — the legal fight has been psychologically exhausting.

The details of the attacks, which the women described in interviews with The New York Times last year, outline a picture of systemic abuse. They were raped, beaten and penetrated with metal objects. One was forced to perform oral sex on several officers. Others were forced to tell jokes as they were being assaulted.

Five of the women were charged with minor offenses and spent as long as two years in jail before their cases were dismissed.

As the women await the court’s ruling, their struggle to deal with the trauma lingers.

“It’s been a very difficult road, since I wasn’t able to get my life back after it happened,” said Claudia Hernández, now 34, weeping, as she testified last month.

She was a political science student at Mexico’s national university at the time, writing a thesis on the Atenco social movement.

“I felt dirty, humiliated, and worthless,” she said.

Ms. Hernández said she still suffered from trauma so great that she could not bear to have children. Her partner keeps asking her to start a family, but she fears that her children could one day face the same sort of abuse, she said.

“I won’t take that risk.”

A version of this article appears in print on , on Page A10 of the New York edition with the headline: Brutalized by the Police, Women Hope for Justice. Order Reprints | Today’s Paper | Subscribe